Equation 677 Database

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Magma c43b4dbf6981…

magma c43b4dbf6981
Size
595
Isomorphism class hash
c43b4dbf6981c76e5b766d210b3ebce5f8e14b3326d24fb5c52e1644e4eaa37a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 09:37:45
Display reorder
133,132,134,129,130,131,119,118,120,121,122,117,469,470,468,473,471,472,484,483,485,481,480,482,371,373,372,376,374,375,524,526,527,569,575,259,260,159,257,258,207,203,154,155,156,152,153,90,89,85,86,87,88,34,33,31,220,221,32,238,237,191,192,135,136,163,162,164,165,166,265,212,270,213,269,210,211,223,177,224,175,222,176,178,71,72,73,74,70,501,503,502,499,498,500,451,450,449,453,454,452,292,291,290,288,289,287,293,295,294,296,297,298,306,305,307,308,309,310,351,350,352,347,348,349,301,300,299,304,302,303,540,546,510,538,533,523,537,555,585,576,588,592,590,554,552,553,106,107,108,103,104,105,63,62,58,59,60,61,15,14,10,11,12,13,141,140,142,143,138,139,127,126,128,123,124,125,53,57,54,55,56,225,228,75,226,227,179,180,251,250,157,252,253,204,181,80,76,77,78,79,400,399,398,397,395,396,317,319,318,322,320,321,478,477,479,475,474,476,323,325,324,326,327,328,333,332,334,329,330,331,509,508,507,504,506,505,424,423,422,421,419,420,534,543,514,525,539,520,547,559,581,571,560,574,565,578,577,586,91,92,93,94,95,96,30,29,25,26,27,28,44,43,45,46,41,42,64,69,65,66,67,68,40,39,35,36,37,38,115,114,116,113,112,274,280,169,281,277,272,273,275,279,168,278,276,271,218,9,5,6,7,8,393,392,394,390,391,389,388,387,386,384,385,383,381,380,382,377,378,379,425,427,426,428,429,430,316,315,314,312,313,311,446,448,447,445,443,444,467,282,283,284,285,286,529,542,511,521,512,513,522,550,566,561,556,594,563,549,548,593,101,102,97,98,99,100,4,217,171,215,172,216,199,198,246,196,247,197,233,187,186,109,110,111,82,81,83,84,229,230,158,256,254,205,206,255,182,231,183,232,184,185,236,190,234,188,235,189,195,242,243,144,244,245,495,494,497,493,496,492,432,431,433,434,435,436,356,358,357,355,353,354,416,418,417,413,414,415,411,410,409,408,412,407,401,403,402,406,404,405,359,361,360,362,363,364,516,545,531,535,532,530,528,583,568,570,558,573,587,557,582,572,47,48,49,50,51,52,160,264,261,161,262,263,193,194,239,240,137,241,219,173,174,23,24,22,3,2,0,1,170,214,249,248,201,202,200,145,146,151,147,148,149,150,19,18,20,21,16,17,167,209,266,267,268,208,460,459,458,457,455,456,368,370,369,367,365,366,346,345,344,342,343,341,464,466,465,461,462,463,441,440,442,437,438,439,486,488,487,491,489,490,340,339,338,337,335,336,536,541,515,519,518,517,544,580,564,567,551,584,562,589,591,579 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = the submagma generated by {0, 36} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 85.

last edited by qawbecrdtey at 2026-10-06 09:37:47 · history